Understanding Quantum Superposition: Can We Observe It?

Quantum mechanics is often shrouded in mystery, particularly when it comes to understanding phenomena like superposition. If a system can be in multiple pure states at once, it is said to be in a superposition. This concept can be explored through the behavior of a photon, a particle of light.

What Is Superposition in Quantum Mechanics?

In quantum mechanics, superposition is represented as a weighted sum of possible states. For instance, a photon can have many possible states, and we can consider a subset where the polarization (the direction of the electric field oscillation) is different. If a photon is moving from west to east, one possibility is vertical polarization, and a 90-degree rotation transforms that to horizontal polarization, north and south.

Creating Superpositions with Photons

Suppose we create an equal superposition of the vertical polarization (State A) and the horizontal polarization (State B). We then obtain a new state (State C) where the photon is polarized at a 45-degree angle to the vertical. Conversely, a superposition where the sign of one state is changed results in State D, a photon polarized at a 45-degree angle to the right of vertical. Interestingly, State A and State B are also superpositions of State C and State D, making the concept of superposition symmetrical.

The Question of Observation

The challenge lies in determining which of these states can be observed. The prompt suggests that this is of great interest because it reflects whether the quantum state is real or just a tool for calculating predictions. Many physicists believe that the quantum state exists in reality. Observing a photon's polarization is tricky because any measurement could have been produced by a photon with a different polarization.

The Impermanence of Polarization States

Unlike classical physics, which predicts that if a system has two distinct states, they can be distinguished through precise measurement, quantum mechanics challenges this notion. Two states at an angle between 0 to 90 degrees cannot be reliably distinguished based on a single example. This makes it difficult to pinpoint the state of a photon through observation alone.

Experimental Filters and Observations

Theoretically, it is possible to create a perfect polarizing filter for a specific polarization plane. In the real world, such filters are imperfect, but quantum mechanics allows for the possibility of having a perfect one. For instance, orienting the filter to allow vertically polarized light guarantees that vertically polarized photons will pass through, while horizontally polarized photons will be blocked.

Once a photon has passed through a vertical polarizing filter, it behaves as if it is vertically polarized. Essentially, the complementary operation to observing it in a certain state (preparing it in a state) is possible. This means that subsequent filters can be used to differentiate between different polarizations of prepared light. However, real-world imperfections mean that about 3 out of every 10,000 photons polarized at one degree away from vertical will not pass through a vertical polarizing filter.

Theoretical Loopholes and Interpretations

There are theoretical loopholes that some might use to argue that the behavior of quantum systems cannot be explained by superposition alone. These loopholes are often referred to by physicists as "loopholes," indicating that such explanations are not preferred. For someone interested in the technical aspects, the PBR theorem (due to Pusey, Barrett, and Rudolph) is worth exploring. This theorem helps validate the physical reality of quantum states and provides a deeper understanding of quantum mechanics.

In conclusion, quantum superposition and its observability continue to be intriguing concepts, with much of the discussion revolving around philosophical questions of reality versus calculation. As technology and experimental methods advance, our understanding of these phenomena is likely to deepen, offering more precise insights into the nature of quantum mechanics.